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Nanoelectronic Devices
Gregory L. Snider
Department of Electrical Engineering
University of Notre Dame
University of Notre Dame
Center for Nano Science and Technology
What are Nanoelectronic Devices?
A rough definition is a device where:
• The wave nature of electrons plays a significant
(dominant) role.
• The quantized nature of charge plays a significant
role.
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Center for Nano Science and Technology
Examples
• Quantum point contacts (QPC)
• Resonant tunneling diodes (RTD)
• Single-electron devices
• Quantum-dot Cellular Automata (QCA)
• Molecular electronics (sometimes not truly nano)
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References
•
Single Charge Tunneling, H. Grabet and M. Devoret, Plenum Press,
New York, 1992
•
Modern Semiconductor Devices, S.M. Sze, John Wiley and Sons,
New York, 1998
•
Theory of Modern Electronic Semiconductor Devices, K. Brennan
and A. Brown, John Wiley and Sons, New York, 2002
•
Quantum Semiconductor Structures, Fundamentals and
Applications , C. Weisbuch and B. Vinter, Academic Press, Inc.,
San Diego, 1991
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When does Quantum Mechanics Play a Role?
W & V, pg. 12, Fig. 5
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More Realistic Confinement
W & V, pg. 13, Fig.6
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Quantum Point Contacts
One of the earliest nanoelectronic devices QPCs depend on ballistic, wavelike transport of carriers through a constriction.
In the first demonstration surface split- gates are used to deplete a 2D
electron gas. The confinement in the constriction produces subbands.
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Quantized Conductance
When a bias is applied from source to drain electrons travel ballisticly.
Each spin-degenerate subband can provide 2e2/h of conductance.
Va Wees, PRL 60, p. 848, 1988
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What About Temperature?
Thermal energy is the bane of all nanoelectronic devices.
T2 > T1
As the temperature increases more subbands become occupied, washing
out the quantized conductance.
All nanoelectronic devices have a characteristic energy that must be larger
than kT
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Resonant Tunnel Devices
In a finite well the wavefunction
penetrates into the walls, which
is tunneling
In the barrier:
n (z)  e
n
z
where
Transmission through a single barrier goes as:

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T e
n 
2m(Vo  E n )

2 n L B
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Two Barriers
Semiclassically a particle in the well
oscillates with:
k
vz 
z
m
It can tunnel out giving a lifetime tn and: E n 
tn
Now 
make a particle incident on the double barrier:

If Ei ≠ En then T = T1T2 which is small
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If Ei = En then the wavefunction builds in the well, as in a Fabry-Perot resonator:
4T1T2
T(E i  E n ) 
(T1  T2 ) 2
Which approaches unity for T1 = T2:

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In Real Life!
Things are, of course, more complicated:
- No mono-energetic injection
- Other degrees of freedom
In the well:
k2
E  En 
2m*
In the leads:
 n3D (E)   3D (E)
dE
E  EF 
exp

 KT 
(2m*) 3 / 2 1/ 2
3D (E) 
E
2 2 3

J
2
q
2
 N(E z )T(E z )dE z
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where
E F  E z 
kTm* 
N(E z ) 
ln 1 exp

 2 
 kT 
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In k Space No One Can Hear You Scream!
For Transmission:
kzo 
2m * (E o  E cL )

To get through the barriers electrons must have E > Ec but must also have the
correct kz. Only states on the disk meet these criteria.
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J is proportional to the number of states on the disk, and therefore to the
area of the disk:
2
2
2
Area  R   kF  kzo 
 J  kF2  kz2o  E FL  E cL  E o  E cL  E FL  E o

 J V

EcL is above Eo, so no
states have the correct kz
Note: we have ignored the transmission probability
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Scattering
Scattering plays an important but harmful role, mixing in-plane and
perpendicular states
B&B p236
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Single Electron Devices
The most basic single-electron device is a single island connected to a lead
through a tunnel junction
The energy required to add one more electron to the island is:
2
EC = e
2C
This is the Charging Energy
If EC > kT then the electron population on the island will be stable.
Usually we want Ec > 3-10 times kT. For room temperature operation
this means C ~ 1 aF.
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If the temperature is too high, the electrons can hop on and off the island
with just the thermal energy. This is uncontrollable.
An additional requirement to quantize the number of electrons on the island
is that the electron must choose whether it is on the island or not.
This requires RT > RK
Where RK = h/e2 ~ 25.8 kΩ
Usually 2-4 times is sufficient
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What is an Island?
• Anywhere that an electron wants to sit can be used
as an island
– Metals
– Semiconductors
• Quantum dots
• Electrostatic confinement
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Single Electron Box
Assume a metallic island
The energy of the configuration with n electrons on the island is :
E(n) =
(ne - Q)2
2(Cs + Cj)
Q = Cs U
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At a charge Q/e of 0.5 one more electron is abruptly added to the island.
What does it mean to have a charge of 1/2 and electron?
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Single - Electron Transistor (SET)
Now the gate voltage U can be used to control the island potential. The
source - drain Voltage V is small but finite.
When U=0, no current flows.
Coulomb Blockade
When (CGU)/e = 0.5 current flows.
Why?
One more electron is allowed on the island.
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These are called Coulomb blockade peaks.
Is the peak the current of only one electron flowing through the island?
No, but they flow through one at a time!
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What about Temperature?
G&D p181
As the temperature increases the peaks stay about the same, while the
valleys no longer go to zero. This is the loss of Coulomb blockade. Finally
the peaks smear out entirely.
This shows the classical regime, such as for metal dots. In semiconductor
dots resonant can cause an increase in the conductance at low
temperatures (the peak values increase).
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SET Stability Diagram
You can also break the Coulomb blockade by applying a large drain voltage.
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Ultra-sensitive electrometers
GD
GE
VG
VE
dot
electrometer
Dot Signal
Add an electron
Lose an electron
Sensitivity can be as high as 10-6 e/sqrt(Hz)
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Single Electron Trap
G&D p123
This non-reversible device can be used to store information.
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Single Electron Turnstile
G&D p124
This is an extension of the single electron trap that can move electrons
one at at time
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Turnstile Operation
Why does it need to be
non-reversible?
G&D page 125
Can this be used as a current standard?
Issues:
Co-tunneling
Missed transitions
Thermally activated events
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Single Electron Pump
Here there are two coupled boxes, and
an electron is moved from one to the
other in a reversible process.
G&D p128
Same Issues:
Missed transitions
Thermally activated events
Co-tunneling
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Background charge effect on single electron devices
Conductance
SET
Vg
e-
Vg
• Nanometer scaled movements of charge in insulators,
located either near or in the device lead to these effects.
• This offset charge noise (Q0) limits the sensitivity of the
electrometer.
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Background charge insensitive single
electron memory
 A bit is represented by a few
electron charge on a floating gate.
 SET electrometer used as a
readout device.
 Random background charge
affects only the phase of the SET
oscillations.
 The FET amplifier solves the
problem of the high output
impedance of the SET transistor.
K. K. Likharev and A. N. Korotkov, Proc. ISDRS’95
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Plasma oxide – fabrication technique
A
Gas inlet
To diffusion pump
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Plasma oxide device
•
Ground
CG
FG
SET
BG
•
•
Two step e-beam
lithography on
PMMA/MMA.
Oxidation after first
step in oxygen plasma
formed by glow
discharge.
Oxide thickness
characterized by VASE
technique.
• 6 nm of oxide grown after 5
min oxidation in 50 mTorr
oxygen plasma at 10 W.
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Hysteresis Loops
•
•
•
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SET conductance
monitored on the
application of a bias on
the control gate.
A back gate bias
cancels the direct
effect of the control
gate on the SET.
The change in the
operating point of the
SET is due to electrons
charging and
discharging the floating
gate.
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Zuse’s paradigm
• Konrad Zuse (1938) Z3 machine
– Use binary numbers to encode
information
– Represent binary digits as on/off state of
a current switch
Telephone
relay
Z3 Adder
on=“1”
off=“0”
The flow through one switch
turns another on or off.
Electromechanical
relay
Vacuum tubes
Solid-state transistors
CMOS IC
Exponential down-scaling
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Problems shrinking the current-switch
Valve shrinks also – hard
to get good on/off
Current becomes small resistance becomes high
Hard to turn next switch
Charge becomes quantized
Power dissipation
threatens to melt
the chip.
New
idea
Quantum Dots
Electromechanical
relay
Vacuum tubes
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Solid-state transistors
CMOS IC
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New paradigm: Quantum-dot
Cellular Automata
Represent information with charge configuration.
Zuse’s paradigm
• Binary
• Current switch
• Charge configuration
Revolutionary, not incremental, approach
Beyond transistors – requires rethinking circuits
and architectures
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Quantum-dot Cellular Automata
Represent binary information by
charge configuration
Cell-cell response function
cell1
A cell with 4 dots
cell2
2 extra electrons
Tunneling between dots
Polarization
Polarization PP== +1
-1
Bit
Bit value
value “1”
“0”
Neighboring cells tend to align.
Coulombic coupling
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cell1
cell2
Bistable, nonlinear cell-cell
response
Restoration of signal levels
Robustness against disorder
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Variations of QCA cell design
4-dot cell
2-dot cell
Indicates path
for tunneling
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5-dot cell
6-dot cell
Middle dot acts as
variable barrier to
tunneling.
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Clocking in QCA
energy
Keyes and Landauer, IBM Journal of Res. Dev. 14, 152, 1970
1
0
x
Clock
0
Clock Applied
Small Input Applied
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Input Removed
0
but Information
is preserved!
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Quasi-Adiabatic Switching
• Clocking Schemes for Nanoelectronics:
•Keyes and Landauer, IBM Journal of Res. Dev. 14, 152, 1970
•Lent et al., Physics and Computation Conference, Nov. 1994
•Likharev and Korotkov, Science 273, 763, 1996
• Requires additional control of cells.
• Introduce a “null” state with zero polarization which encodes no
information, in contrast to “active” state which encodes binary 0 or 1.
Clocking achieved by modulating
barriers between dots (as in
semiconductor dot case)
P= +1
P= –1
Null State
Clocking achieved by modulating
energy of third state directly (as
in metallic or molecular case)
Clocking signal should not have to be sent to individual cells, but to sub-arrays of cells.
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Microprocessor power continues to increase exponentially
100000
10000
Power (Watts)

Power Will Be a Limiter
1000
Transition
from NMOS
to CMOS
18KW
5KW
1.5KW
500W
Pentium®
P6
286
486
10
8086
386
8080
8008 8085
1
4004
100
0.1
1971 1974 1978 1985 1992 2000 2004 2008

Power delivery and dissipation will be prohibitive !
Source: Borkar & De, Intel
Slide author: Mary Jane Irwin, Penn State University
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Power Density will
Increase
Sun’s
Surface
Power Density (W/cm2)
10000

Rocket
1000
Nuclear
Reactor
100
10
Nozzle
8086
Hot Plate
P6
8008
Pentium®
8085
4004
386
286
486
8080
1
1970
1980
1990
2000
2010
Power densities too high to keep junctions at low temps
Source: Borkar & De, Intel
Slide author: Mary Jane Irwin, Penn State University
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QCA power dissipation
QCA architectures can operate at densities above 1011 devices/cm2
without melting the chip.
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QCA devices
Binary wire 10
Majority gate
0
1
Inverter
1
0
A
B
C
0
1
M
A
B
Out
C
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Programmable 2-input
AND or OR gate.
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Metal-dot QCA implementation
Metal tunnel junctions
Al/AlO2 on
SiO2
electrometers
1 µm
“dot” = metal island
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70 mK
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Tunnel junctions by shadow evaporation
Thin
Second
First
Oxidation
Al/AlO
aluminum
aluminum
oftunnel
aluminum
deposition
deposition
junction
x/Al
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Metal-dot QCA cells and devices
• Demonstrated 4-dot cell
Input Double Dot
Switch Point
(1,0)
(0,1)
Top Electrometer
Bottom Electrometer
A.O. Orlov, I. Amlani, G.H. Bernstein, C.S. Lent, and G.L. Snider, Science, 277, pp. 928-930, (1997).
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Switching of 4-Dot Cell
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Majority Gate
A
B
C
M
Amlani, A. Orlov, G. Toth, G. H. Bernstein, C. S. Lent, G. L. Snider, Science 284, pp. 289-291 (1999).
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QCA Latch Fabrication
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QCA Clocked Latch (Memory)
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QCA Shift Register
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Fan-Out
VClock2
Vin+
VClock1
Vin–
V Clock2
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From metal-dot to molecular QCA
Metal tunnel junctions
“dot” = metal island
70 mK
“dot” = redox center
Mixed valence compounds
room temperature+
Metal-dot QCA established proof-of-principle.
but …low T, fabrication variations
Molecular QCA: room temp, synthetic consistency
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Charge configuration represents bit
HOMO
“1”
“0”
isopotential
surface
Gaussian 98 UHF/STO-3G
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Double molecule
Considered as a single cell, bit is represented by
quadrupole moment.
Alternatively: consider it a dipole driving another dipole.
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Double molecule
“1”
HOMO
Isopotential (+)
“0”
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Core-cluster molecules
Five-dot cell
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Core-cluster moleculesTheory of
molecular QCA bistability Allyl group
Variants with
“feet” for
surface binding
and orientation
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Electron Switching in QCA
Molecular Dots
Metal Dots
Measure conductance
Measure capacitance
C
Voltage
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Electron Switching Demonstration
Capacitance peaks correspond to “clickclack” switching within the molecule
JACS 125, 15250-15259, 2003
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Clocked molecular QCA
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Summary
• QCA may offer a promising paradigm for nanoelectronics
–
–
–
–
–
–
binary digits represented by charge configuration
beyond transistors
general-purpose computing
enormous functional densities
solves power issues: gain and dissipation
Scalable to molecular dimensions
• Single electron memories represent the ultimate scaling
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